Computational Science and Techniques

A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown.

It is important for an organization to know what capability/maturity of the process a chosen methodology could ensure. This paper is focused on DSDM Atern process maturity by CMMI.

Computational modeling of a biosensor with allosteric enzyme layer was investigated in this study. The operation of the biosensor is modeled using non-stationary reaction-diffusion equations. The model involves three regions: the allosteric enzyme layer where the allosteric enzyme reactions as well as then mass transport by diffusion take place, the diffusion region where the mass transport by diffusion and non-enzymatic reactions take place and the convective region in which the analyte concentration is maintained constant. The biosensor response on dependency substrate concentration, cooperativity coefficient and the diffusion layer thickness on the same parameters have been studied.

In this research, parallel computing capabilities of MATLAB and the capabilities for the finite element method were analyzed. A program for solving a heat transfer problem by the finite element method was implemented. Three different parallel algorithms using CPU and GPU for solving steady state and transient heat transfer problems were proposed and implemented. A maximal speedup of around 2.3 times for steady state and 2 times for transient problem solving time was achieved by using a quad-core CPU.

This work contains Monte–Carlo Markov Chain algorithm for estimation of multi-dimensional rare events frequencies. Logits of rare event likelihood we are modeling with Poisson distribution, which parameters are distributed by multivariate normal law with unknown parameters – mean vector and covariance matrix. The estimations of unknown parameters are calculated by the maximum likelihood method. There are equations derived, those must be satisfied with model’s maximum likelihood parameters estimations. Positive definition of evaluated covariance matrixes are controlled by calculating ratio between matrix maximum and minimum eigenvalues.